Ok, Im going to say Alex's because twe all love that place. But what about The Pike on 4th? They get an interesting variey of bands and they have that innovative bring your MP3 night.
DiPiazza's on PCH has bands pretty much every night. I like going there since I am a smoker and they have a smoking area that I can still drink in. I also am a little bias because I usually don't have to pay to get in. Love the owners too!!
Observation Bar is a favorite of mine... the Sky Room though it's small both places have an amazing view of Long Beach. I also like that place hidden in the back of Marina Pacificia Tantalum... Fun yummy Mi Ti's